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Support among Americans for President Bush’s handling of the Iraq war has fallen, but analysts think that after the United States turns over sovereignty to the Iraqis next month and the prisoner-abuse scandal fades, Mr. Bush’s approval ratings will rise and impact the presidential campaign.

A CNN/Time poll released Friday shows Mr. Bush’s job-approval rating at 46 percent, down from 63 percent in December after Saddam Hussein was captured.

Despite the pounding his war policies have undergone in the past month, especially since the sharp rise in troop casualties from the insurgency against U.S. occupation in Iraq, Mr. Bush still has two major factors in his favor in most voter surveys: A majority of Americans support U.S. troops’ helping Iraq obtain democracy, and Mr. Bush is seen as stronger than Democratic challenger Sen. John Kerry on ensuring America’s national security.

A 53 percent majority continues to support the presence of U.S. troops in Iraq to help put that country on the road to democratic reform, according to a nationwide poll conducted by the Pew Research Center last week.

“Americans favor keeping troops there until a stable government is established. That number has changed little since early April, after four U.S. contractors were murdered and their bodies desecrated,” the Pew survey said.

Most voters by a significant margin continue to favor Mr. Bush over Mr. Kerry “when it comes to defending the country from future terrorism (52 percent for Bush versus 33 percent for Mr. Kerry),” Pew said. Throughout the debate over Iraq, Mr. Bush has linked U.S. efforts there to the war on terrorism and to homeland security.

No one doubts that if events worsen in Iraq, the fallout will continue to erode Mr. Bush’s public support and undermine his chances of winning a second term. But analysts think that the situation there willimprove in the months to come — especially when the United States turns over governing power to an interim Iraqi government on June 30.

“Bush’s great liability is that he is associated with the policy that seems to be failing. If these things get worse or stay the way it’s been in the past two months, I think Bush becomes the underdog in November,” said foreign-policy analyst Michael O’Hanlon of the Brookings Institution.

“But even though I support Kerry, I think it’s more likely that we will see modest improvement in Iraq and, therefore, an extremely closer race,” he said.

Although Mr. Bush’s job-approval ratings have dropped in recent weeks, partly as a result of events in Iraq, he still draws higher marks than Mr. Kerry on national security and on leadership issues, both critical concerns in an era when most Americans say they expect another terrorist attack on the United States.

“Voters continue to view Bush as a strong leader and possessing good judgement in a crisis,” the Pew poll said. “Roughly half of voters say these descriptions apply to Bush; only about a third say they better describe Kerry.”

More important politically in a close election, Mr. Bush “holds a significant advantage on these personal qualities among swing voters,” the poll said. “More than half of swing votes (54 percent) view Bush as a strong leader; just 14 percent say that phrase better describes Kerry. Similarly, by four-to-one (53 percent to 13 percent) swing voters view Bush, not Kerry, as using good judgements in a crisis.”

Republican pollster Whit Ayres said a poll he conducted at the height of the prisoner-abuse story suggested that the scandal did not affect how Americans viewed Iraq, as much as news reports seemed to suggest.

“It showed that Americans were proud rather than ashamed of our overall effort in Iraq by a margin of 20 percentage points — 49 percent to 29 percent. That tells me that Americans are putting this whole prisoner-abuse story in the broader context of what we accomplished in Iraq with the removal of Saddam Hussein,” he said.